Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
490 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #127×D151 | C2 | semidirect |
| 2. #23752744 | C2 | semidirect |
| 3. #23752600 | C2 | semidirect |
| 4. #23752575 | C2 | semidirect |
| 5. #23752413 | C2 | semidirect |
| 6. #23752409 | C2 | semidirect |
| 7. #23752407 | C2 | semidirect |
| 8. #23752364 | C2 | semidirect |
| 9. #23752344 | C2 | semidirect |
| 10. #23752268 | C2 | semidirect |
| 11. #459×C151 | C2 | semidirect |
| 15. C2×#14558993 | C22 | semidirect |
| 16. C2×#14558992 | C22 | semidirect |
| 17. C2×#14558989 | C22 | semidirect |
| 23. #18012730 | C22 | semidirect |
| 24. #18012726 | C22 | semidirect |
| 28. C4×Dic302 | C22 | semidirect |
| 32. C4⋊(C151⋊C8) | C22 | semidirect |
| 33. #18012661 | C22 | semidirect |
| 34. #18012660 | C22 | semidirect |
| 35. #18012659 | C22 | semidirect |
| 37. #18012649 | C22 | semidirect |
| 38. C2×D8×C151 | C22 | semidirect |
| 40. C4×D4×C151 | C22 | semidirect |
| 41. C4⋊C8×C151 | C22 | semidirect |
| 42. #102×C151 | C22 | semidirect |
| 156. C151 | #3217 | semidirect |
| 165. #459 | D151 | semidirect |
| 175. C2×D8 | C2×D151 | semidirect |
| 189. C4×D4 | C2×D151 | semidirect |
| 193. C4⋊C8 | C2×D151 | semidirect |
| 197. #102 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #127×D151 | 2 |
| #23752744 | 2 |
| #23752600 | 2 |
| #23752575 | 2 |
| #23752413 | 2 |
| #23752409 | 2 |
| #23752407 | 2 |
| #23752364 | 2 |
| #23752344 | 2 |
| #23752268 | 2 |
| #459×C151 | 2 |
| #3217 | 151 |